सोडोवचें {c}{5x-y+2z=7}{-2x+6y+9z=0}{-7x+5y-3z=-7}

$$\left. \begin{array} { c } { 5 x - y + 2 z = 7 } \\ { - 2 x + 6 y + 9 z = 0 } \\ { - 7 x + 5 y - 3 z = - 7 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = \frac{21}{13} = 1\frac{8}{13} \approx 1.615384615$$

$$y=\frac{10}{13}\approx 0.769230769$$

$$z=-\frac{2}{13}\approx -0.153846154$$

बदली वापरून संक्षिप्त पांवडे

y खातीर 5x-y+2z=7 सोडोवचो.

$$y=5x+2z-7$$

दुस-या आनी तिस-या समिकरणांत y खातीर 5x+2z-7 बदलपी घेवचो.

$$-2x+6\left(5x+2z-7\right)+9z=0 -7x+5\left(5x+2z-7\right)-3z=-7$$

अनुक्रमान x आनी z खातीर हीं समिकरणां सोडोवचीं.

$$x=\frac{3}{2}-\frac{3}{4}z z=4-\frac{18}{7}x$$

z=4-\frac{18}{7}x ह्या समिकरणांत x खातीर \frac{3}{2}-\frac{3}{4}z बदलपी घेवचो.

$$z=4-\frac{18}{7}\left(\frac{3}{2}-\frac{3}{4}z\right)$$

z खातीर z=4-\frac{18}{7}\left(\frac{3}{2}-\frac{3}{4}z\right) सोडोवचो.

$$z=-\frac{2}{13}$$

x=\frac{3}{2}-\frac{3}{4}z ह्या समिकरणांत z खातीर -\frac{2}{13} बदलपी घेवचो.

$$x=\frac{3}{2}-\frac{3}{4}\left(-\frac{2}{13}\right)$$

x=\frac{3}{2}-\frac{3}{4}\left(-\frac{2}{13}\right) तल्यान x मेजचो.

$$x=\frac{21}{13}$$

x आनी -\frac{2}{13} ह्या समिकरणांत z खातीर \frac{21}{13} बदलपी घेवचो y=5x+2z-7.

$$y=5\times \frac{21}{13}+2\left(-\frac{2}{13}\right)-7$$

y=5\times \frac{21}{13}+2\left(-\frac{2}{13}\right)-7 तल्यान y मेजचो.

$$y=\frac{10}{13}$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{21}{13} y=\frac{10}{13} z=-\frac{2}{13}$$